The Poincare'-Lyapounov-Nekhoroshev theorem for involutory systems of vector fields

TL;DR

This paper generalizes the Poincare'-Lyapounov-Nekhoroshev theorem to encompass non-abelian involutory systems of vector fields and broader invariant manifolds, expanding its applicability beyond torus actions.

Contribution

It introduces a new extension of the theorem to non-abelian involutory systems and general invariant manifolds, broadening the scope of the original theorem.

Findings

Extended theorem to non-abelian systems

Applicable to general invariant manifolds

Broadened understanding of involutory systems

Abstract

We extend the Poincare'-Lyapounov-Nekhoroshev theorem from torus actions and invariant tori to general (non-abelian) involutory systems of vector fields and general invariant manifolds.